Question: Solve for $x$ : $6\sqrt{x} + 8 = 8\sqrt{x} + 5$
Solution: Subtract $6\sqrt{x}$ from both sides: $(6\sqrt{x} + 8) - 6\sqrt{x} = (8\sqrt{x} + 5) - 6\sqrt{x}$ $8 = 2\sqrt{x} + 5$ Subtract $5$ from both sides: $8 - 5 = (2\sqrt{x} + 5) - 5$ $3 = 2\sqrt{x}$ Divide both sides by $2$ $\frac{3}{2} = \frac{2\sqrt{x}}{2}$ Simplify. $\dfrac{3}{2} = \sqrt{x}$ Square both sides. $\dfrac{3}{2} \cdot \dfrac{3}{2} = \sqrt{x} \cdot \sqrt{x}$ $x = \dfrac{9}{4}$